Solve for $x$ : $x^2 + 12x + 27 = 0$
Solution: The coefficient on the $x$ term is $12$ and the constant term is $27$ , so we need to find two numbers that add up to $12$ and multiply to $27$ The two numbers $3$ and $9$ satisfy both conditions: $ {3} + {9} = {12} $ $ {3} \times {9} = {27} $ $(x + {3}) (x + {9}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x + 3) (x + 9) = 0$ $x + 3 = 0$ or $x + 9 = 0$ Thus, $x = -3$ and $x = -9$ are the solutions.